Most cited papers in Numerical methods in inverse problems
What are the most cited papers in Numerical methods in inverse problems?
The most cited paper in Numerical methods in inverse problems is "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems" (Amir Beck, Marc Teboulle, 2009), with 12,347 citations. Next come "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint" (5,044) and "Function minimization by conjugate gradients" (4,962).
Showing 50 of 100 papers. Every paper with more than 670 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems Amir Beck, Marc Teboulle · SIAM Journal on Imaging Sciences | 2009 | 12,347 |
| 2 | An iterative thresholding algorithm for linear inverse problems with a sparsity constraint Ingrid Daubechies, Michel Defrise, Christine De Mol · Communications on Pure and Applied Mathematics | 26 Aug 2004 | 5,044 |
| 3 | Function minimization by conjugate gradients Roger Fletcher · The Computer Journal | Feb 1964 | 4,962 |
| 4 | A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging Antonin Chambolle, Thomas Pock · Journal of Mathematical Imaging and Vision | 20 Dec 2010 | 4,454 |
| 5 | The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems Per Christian Hansen, Dianne Prost O’Leary · SIAM Journal on Scientific Computing | Nov 1993 | 3,155 |
| 6 | Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles Léon Van Hove · Physical Review | Jul 1954 | 2,840 |
| 7 | A constrained regularization method for inverting data represented by linear algebraic or integral equations Stephen W. Provencher · Computer Physics Communications | Sep 1982 | 2,712 |
| 8 | Signal Recovery by Proximal Forward-Backward Splitting Patrick L. Combettes, Valérie R. Wajs · Multiscale Modeling and Simulation | 2005 | 2,708 |
| 9 | Proximal Splitting Methods in Signal Processing Patrick L. Combettes, Jean‐Christophe Pesquet · Springer optimization and its applications | 2011 | 2,237 |
| 10 | Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II Luis Álvarez, Pierre-Louis Lions, Jean‐Michel Morel · SIAM Journal on Numerical Analysis | Jun 1992 | 2,221 |
| 11 | An Interior-Point Method for Large-Scale -Regularized Least Squares Seung-Jean Kim, Kwangmoo Koh, Michael S. Lustig et al. · IEEE Journal of Selected Topics in Signal Processing | Dec 2007 | 2,107 |
| 12 | A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration José M. Bioucas‐Dias, Mário A. T. Figueiredo · IEEE Transactions on Image Processing | 21 Nov 2007 | 2,100 |
| 13 | Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems Amir Beck, Marc Teboulle · IEEE Transactions on Image Processing | 28 Jul 2009 | 2,056 |
| 14 | Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm Irina F. Gorodnitsky, Bhaskar D. Rao · IEEE Transactions on Signal Processing | Mar 1997 | 1,857 |
| 15 | An Iterative Regularization Method for Total Variation-Based Image Restoration Stanley Osher, Martin Burger, Donald Goldfarb et al. · Multiscale Modeling and Simulation | 2005 | 1,827 |
| 16 | On a quasi-linear parabolic equation occurring in aerodynamics Julian D. Cole · Quarterly of Applied Mathematics | Oct 1951 | 1,765 |
| 17 | REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems Per Christian Hansen · Numerical Algorithms | Mar 1994 | 1,734 |
| 18 | The Fractional Order Fourier Transform and its Application to Quantum Mechanics Victor Namias · IMA Journal of Applied Mathematics | 1980 | 1,722 |
| 19 | Total Generalized Variation Kristian Bredies, Karl K. Kunisch, Thomas Pock · SIAM Journal on Imaging Sciences | 2010 | 1,567 |
| 20 | The Resolving Power of Gross Earth Data George Backus, Freeman Gilbert · Geophysical Journal International | Oct 1968 | 1,540 |
| 21 | Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods Hédy Attouch, Jérôme Bolte, Benar Fux Svaiter · Mathematical Programming | 19 Aug 2011 | 1,494 |
| 22 | The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems E Weinan, Bing Yu · Communications in Mathematics and Statistics | 14 Feb 2018 | 1,471 |
| 23 | Smoothing noisy data with spline functions Grace Wahba · Numerische Mathematik | Oct 1975 | 1,471 |
| 24 | Nonlinear Schr�dinger equations and sharp interpolation estimates Michael I. Weinstein · Communications in Mathematical Physics | Dec 1983 | 1,451 |
| 25 | A multiprojection algorithm using Bregman projections in a product space Yair Censor, Tommy Elfving · Numerical Algorithms | Sep 1994 | 1,384 |
| 26 | Gradient methods for minimizing composite functions Yu. Nesterov · Mathematical Programming | 20 Dec 2012 | 1,383 |
| 27 | Training with Noise is Equivalent to Tikhonov Regularization Chris M. Bishop · Neural Computation | 1995 | 1,352 |
| 28 | Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth Luis A. Caffarelli, Basilis Gidas, Joel Spruck · Communications on Pure and Applied Mathematics | Apr 1989 | 1,346 |
| 29 | A unified treatment of some iterative algorithms in signal processing and image reconstruction Charles L. Byrne · Inverse Problems | 14 Nov 2003 | 1,343 |
| 30 | Exact Reconstruction of Sparse Signals via Nonconvex Minimization Rick Chartrand · IEEE Signal Processing Letters | 17 Sep 2007 | 1,315 |
| 31 | Boundary regularity for solutions of degenerate elliptic equations Gary M. Lieberman · Nonlinear Analysis | Nov 1988 | 1,306 |
| 32 | Regularity of the obstacle problem for a fractional power of the laplace operator Luís Silvestre · Communications on Pure and Applied Mathematics | 9 Aug 2006 | 1,281 |
| 33 | On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction Christomir Christov · Mechanics Research Communications | 9 Dec 2008 | 1,256 |
| 34 | Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems Kenichi Sakamoto, Masahiro Yamamoto · Journal of Mathematical Analysis and Applications | 30 Apr 2011 | 1,238 |
| 35 | Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality Hédy Attouch, Jérôme Bolte, Patrick Redont et al. · Mathematics of Operations Research | 30 Apr 2010 | 1,234 |
| 36 | A general theory of heat conduction with finite wave speeds Morton E. Gurtin, ALLEN C. PIPKIN · Archive for Rational Mechanics and Analysis | 1968 | 1,221 |
| 37 | Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method Weng Cho Chew, Y.M. Wang · IEEE Transactions on Medical Imaging | Jun 1990 | 1,131 |
| 38 | Lebesgue and Sobolev Spaces with Variable Exponents Vicentiu D. Radulescu, Dusan D. Repovs | 11 Jun 2015 | 1,094 |
| 39 | Nonmonotone Spectral Projected Gradient Methods on Convex Sets Ernesto G. Birgin, José Mario Martínez, Marcos Raydan · SIAM Journal on Optimization | 2000 | 1,093 |
| 40 | $L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver Zongben Xu, Xiangyu Chang, Fengmin Xu et al. · IEEE Transactions on Neural Networks and Learning Systems | 29 May 2012 | 1,089 |
| 41 | Inverse Heat Transfer: Fundamentals and Applications MN Ozisik, HRB Orlande, A.J. Kassab · Applied Mechanics Reviews | 2002 | 1,085 |
| 42 | Non-linear elliptic and parabolic equations involving measure data Lucio Boccardo, Thierry Gallouët · Journal of Functional Analysis | Nov 1989 | 1,059 |
| 43 | MoDL: Model-Based Deep Learning Architecture for Inverse Problems Hemant K. Aggarwal, Merry P. Mani, Mathews Jacob · IEEE Transactions on Medical Imaging | 13 Aug 2018 | 1,053 |
| 44 | Tikhonov Regularization and Total Least Squares Gene Howard Golub, Per Christian Hansen, Dianne Prost O’Leary · SIAM Journal on Matrix Analysis and Applications | 1999 | 1,049 |
| 45 | Minimax estimation via wavelet shrinkage David L. Donoho, Iain M. Johnstone · The Annals of Statistics | Jun 1998 | 1,031 |
| 46 | Image Restoration by the Method of Convex Projections: Part 1ߞTheory Dante C. Youla, H. Webb · IEEE Transactions on Medical Imaging | Oct 1982 | 1,030 |
| 47 | Fading memory and the problem of approximating nonlinear operators with Volterra series Stephen Boyd, Leon Ong Chua · IEEE Transactions on Circuits and Systems | Nov 1985 | 1,001 |
| 48 | Basic error estimates for elliptic problems Philippe G. Ciarlet · Handbook of numerical analysis | 1991 | 988 |
| 49 | Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit Deanna Needell, Roman Vershynin · Foundations of Computational Mathematics | 4 Jun 2008 | 960 |
| 50 | Curvature and the eigenvalues of the Laplacian Henry P. McKean, I. M. Singer · Journal of Differential Geometry | 1967 | 955 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.